The US Postal Service will accept a box for domestic shipment only if the sum of

Question

The US Postal Service will accept a box for domestic shipment only if the sum of its length and girth (distance around) is does not exceed 108 inches. What are the dimen- sions of the cylindrical box (circular cross section, closed ends) with largest volume that can be shipped in the US Mail? the dimensions are x=18 and y=36 but, Explain how you know for sure that the dimensions you found give the box with the largest rather than the smallest volume? and Students often describe their method for solving optimization problems as "set the derivative equal to zero and solve for x." Is the solution to an optimization problem always a point where the derivative is zero? If so, explain why. If not, explain why not.

Explanation / Answer

108 >= 4x + y V = yx^2 = (108-4x)x^2 = 108x^2 - 4x^3 V' = 216x - 12x^2 = 0 x = 216/12 = 18 y = 108 - 4*18 = 36 V = 36*18^2 = 11664 from a box of 18X18X36

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.